Optics of semiconductors from meta-GGA-based time-dependent density-functional theory

TL;DR

This paper demonstrates that using meta-GGA exchange-correlation functionals in time-dependent density functional theory yields highly accurate optical spectra for silicon and germanium, thanks to the singularity support in the kernel.

Contribution

It introduces the use of meta-GGA functionals in TDDFT, revealing their ability to accurately capture optical properties of semiconductors by supporting a key singularity.

Findings

Excellent agreement with experimental spectra

Meta-GGA kernel supports a $\alpha/q^2$ singularity

Enables better handling of non-local exchange-correlation effects

Abstract

We calculate the optical spectra of silicon and germanium in the adiabatic time-dependent density functional formalism, making use of kinetic energy density-dependent (meta-GGA) exchange-correlation functionals. We find excellent agreement between theory and experiment. The success of the theory on this notoriously difficult problem is traced to the fact that the exchange-correlation kernel of meta-GGA supports a singularity of the form $\alpha/q^2$ (where $q$ is the wave-vector and $\alpha$ is a constant), whereas previously employed approximations (e.g. local density and generalized gradient approximations) do not. Thus, the use of the adiabatic meta-GGA opens a new path for handling the extreme non-locality of the time-dependent exchange-correlation potential in solid-state systems.